Problem: Solve: $\dfrac{5}{6} + \dfrac{3}{4} + \dfrac{2}{3} = $
Answer: Let's look at the multiples of each denominator and see which multiples they have in common. Denominator Multiples ${6}$ $6, \underline{{12}}, 18$ ${4}$ $4, 8, \underline{{12}}, 16$ ${3}$ $3, 6, 9, \underline{{12}}$ The least common multiple is ${12}$. Let's use multiplication to make each fraction have a denominator of $12$. $\begin{aligned} &{\dfrac{5}{6}}=\dfrac{{5} \times 2}{{6} \times2} = {\dfrac{10}{12}}\\\\ &{\dfrac{3}{4}}=\dfrac{{3} \times 3}{{4} \times3} = {\dfrac{9}{12}}\\\\ &{\dfrac{2}{3}}=\dfrac{{2} \times 4}{{3} \times4} = {\dfrac{8}{12}} \end{aligned}$ $\begin{aligned} &{\dfrac{5}{6}} + {\dfrac{3}{4}} + {\dfrac{2}{3}}\\\\ =& {\dfrac{10}{12}} + {\dfrac{9}{12}} + {\dfrac{8}{12}}\\\\ =&\dfrac{{10} + {9} + {8}}{12}\\\\ =&\dfrac{19 + 8}{12}\\\\ =&\dfrac{27}{12} \end{aligned}$ ${\dfrac{5}{6}} +{\dfrac{3}{4}} +{\dfrac{2}{3}} = \dfrac{27}{12}$ $\dfrac{27}{12}$ can also be written as $\dfrac{9}{4}$, or $2\dfrac14$.